Physical Review B
The theory of diffusion-controlled correlated reaction kinetics is developed for the radiation boundary condition (RBC) at the reaction surface. Limited only by the assumptions of purely radial spatial dependence, of a spherical reaction surface, and of continuum diffusion, these results comprise a complete solution for these kinetics. The limiting solutions are obtained for the case of the Smoluchowski boundary condition (SBC) at the reaction surface; numerical solutions are presented, as are the analytic forms of certain limiting cases. The initial recovery for the RBC is linear in time, whereas for the SBC it is well known to be proportional to the square root of time. The discussion is presented in the context of radiation damage in solids, although the results are applicable to other fast-kinetics systems, e.g., radiation and photophysics, chemistry, and biology.
D. Peak and J.W. Corbett, "Diffusion-Controlled Reaction Kinetics," Physical Review B 5(4), 1226- 1238 (1972). DOI: 10.1103/PhysRevB.5.1226